Representations for Green's functions suitable for water-wave problems involving
porous structures are obtained by integrating solutions to appropriate heat conduction
problems with respect to time. By utilizing different representations for these
heat equation solutions for small and large times, the changeover being determined
by an arbitrary positive parameter a, a one-parameter family of formulas for the
required Green's function is derived and by varying a the convergence characteristics
of this new representation can be altered. Letting a --> 0 results in known
eigenfunction expansions. The results of computations are presented showing the
accuracy and effciency of the resulting formulas.